Entangling characterization of (SWAP)1/m and Controlled unitary gates
S.Balakrishnan, R.Sankaranarayanan
TL;DR
This paper analyzes the entangling capabilities of (SWAP)1/m and controlled unitary gates, identifying the unique perfect entangler in the family and characterizing the entangling power of certain controlled gates.
Contribution
It demonstrates that only (SWAP)1/2 is a perfect entangler among (SWAP)1/m and identifies a subset of controlled unitaries equivalent to CNOT with maximum entangling power.
Findings
(SWAP)1/2 is the only perfect entangler in the family.
A subset of controlled unitaries equivalent to CNOT are perfect entanglers.
Perfect entanglers must have maximum entangling power.
Abstract
We study the entangling power and perfect entangler nature of (SWAP)1/m, for m>=1, and controlled unitary (CU) gates. It is shown that (SWAP)1/2 is the only perfect entangler in the family. On the other hand, a subset of CU which is locally equivalent to CNOT is identified. It is shown that the subset, which is a perfect entangler, must necessarily possess the maximum entangling power.
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